I never knew that it was ever considered for AZ and NM to merge. It's better that they both remained separate, though, since they're both pretty unique.
It appears that it was part of a political deal. Admission of Dakota, Washington, and Montana was blocked by the Democrats. When the Republicans had a landslide victory in 1888, they pushed through statehood for those states, including the division of Dakota, and threw in Idaho and Wyoming for good measure - even though they didn't really have the population to support statehood.
Teddy Roosevelt had an affinity for New Mexico since a large number of the Roughriders had come from there. At their first reunion, which was held in Las Vegas, he was persuaded to back statehood. There was a concern that Arizona and New Mexico might elect Democrat senators. Some Republicans favored statehood and some were opposed. Senator Quay from Pennsylvania, for whom Quay County is named, favored statehood - but he also had business interests there. There was probably also a racial aspect as well. Some may have hoped that Arizona would help "Americanize" the state.
The bill that provided for the election in Arizona and New Mexico was also the same one that provided for statehood for a combination of Oklahoma and Indian territories. So it may have simply been a concoction of a formula that would permit completion of statehood coverage for the continental US. I have found the text of the bill, but only for the sections that pertain to Oklahoma. There was no election in Oklahoma and Indian Territory, but simply a constitutional convention that led to accession to the Union as 46th State in 1907.
The merged state would have been called Arizona. Voters in New Mexico appeared to support because they believed it was the only way they were going to get statehood (plus they had about 50% more population). Arizonans were told that it could be a long time before they achieved statehood because of their lack of population, but still voted it down.
The delegates elected to the constitutional convention for the joint state in New Mexico went ahead and met on an unofficial basis, but didn't develop a constitution. The leading opponent of statehood, Senator Albert Beveridge of Indiana was defeated for re-election in 1910 when the Democrats took control of the legislature. Beveridge was the keynote speaker at the Bull Moose convention in 1912, and may have had enough influence over Roosevelt to get him to accept the joint state proposal. Statehood for both states was part of the Republican platform in 1908 and was given backing by Taft.
Incidentally, the apportionment following the 1910 census provided for 433 representatives, plus one each for New Mexico and Arizona when/if they entered the Union. When they did this made 435. After Congress failed to reapportion after the 1920 census, it got stuck at 435, so that now 100 years later it commonly thought to be a fixed number. When Hawaii and Alaska entered the Union, they were apportioned one representative each, but with a specific provision to revert to 435 after the 1960 census.
New Mexico had been fairly close to statehood several times earlier. In 1850, New Mexicans had drafted a state constitution. However it was specifically anti-slavery. The 1849 gold rush had brought too many northerners to California to extend slavery there, and it had been hoped that New Mexico would be admitted as a slave state to balance California. As part of the Compromise of 1850, California was admitted as a free state, Utah and New Mexico territories were created with popular sovereignty on the slavery issue, and the border between Texas and New Mexico settled.
In 1875 a proposal for statehood had been approved by both houses of Congress, parallel to those that resulted in Colorado joining the Union. There were slight differences between the two houses. It was late in the session, and a 2/3 majority was required for the House to consider concurring with the Senate amendments. The delegate from New Mexico was particularly gregarious. A Michigan congressman had just given a speech advocating a civil rights law, when the New Mexico delegate happened to enter the chamber. Seeing the other (Republican) members congratulating the Michigan representative, the New Mexico delegate rushed on to the floor to vigorously shake his hand. This enraged enough southern representatives, that the 2/3 vote was not secured.
And in 1895, there were parallel proposals for Utah and New Mexico statehood. The delegate from New Mexico contracted malaria, but was told that Congress would recess before the House committee would consider the matter, and so he returned to the drier climate of New Mexico. For some reason, Congress continued in session longer than expected. When the committee met to consider the statehood measures, the Utahn delegate was present and secured approval of his bill which was then passed by the House. Since the New Mexico delegate was not present, his bill was not considered. It later was approved by the House, but had been delayed too long to get Senate approval.
